@article{Liu2016, 
author = {Longfei Liu and Xiaoyuan Yang and Xiaoni Du and Bin Wei},
title = {On the Linear Complexity of New Generalized Cyclotomic Binary Sequences of Order Two and Period pqr},
year = {2016},
journal = {Tsinghua Science and Technology},
volume = {21},
number = {3},
pages = {295-301},
keywords = {stream cipher, pseudorandom sequence, generalized cyclotomy, linear complexity},
url = {https://www.sciopen.com/article/10.1109/TST.2016.7488740},
doi = {10.1109/TST.2016.7488740},
abstract = {Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd(p–1, q–1)=gcd(p–1, r–1)=gcd(q–1, r–1)=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF(2) is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks.}
}